Additive model. Time series expressed as the sum of several components:
\(Y_t = T_t + C_t + S_t + I_t\).
- Trend (T): long-term growth or decline, here linear with slope β.
- Cycle (C): multiyear oscillation simulated with a sinusoid of amplitude A and period P.
- Seasonality (S): fixed intra-annual pattern; indices based at 100 (T1–T4) are added additively.
- Irregular (I): structured noise generated as AR(p): \(I_t = \sum_{k=1}^{p} \varphi_k I_{t-k} + \varepsilon_t\) with \(\varepsilon_t \sim \mathcal N(\mu,\sigma^2)\).